# Fast and Accurate Computation of Gauss-Legendre and Gauss-Jacobi Quadrature Nodes and Weights

@article{Hale2013FastAA,
title={Fast and Accurate Computation of Gauss-Legendre and Gauss-Jacobi Quadrature Nodes and Weights},
author={Nicholas Hale and Alex Townsend},
journal={SIAM J. Sci. Comput.},
year={2013},
volume={35}
}
• Published 6 March 2013
• Computer Science
• SIAM J. Sci. Comput.
An efficient algorithm for the accurate computation of Gauss--Legendre and Gauss--Jacobi quadrature nodes and weights is presented. The algorithm is based on Newton's root-finding method with initial guesses and function evaluations computed via asymptotic formulae. The $n$-point quadrature rule is computed in $\mathcal{O}(n)$ operations to an accuracy of essentially double precision for any $n\geq 100$.
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